论文标题
光谱共生的Lyapunov指数，用于两个字母的二级替代的拓扑因素
Lyapunov exponents of the spectral cocycle for topological factors of bijective substitutions on two letters
论文作者
论文摘要
本文探讨了由A. Bufetov和B. Solomyak定义的光谱合过程，在两个字母上的Bioxtive取代的特殊情况下，最突出的例子是Thue-Morse的替代。我们得出了与预期指数行为偏差的明确次数行为。此外，这些尖锐的边界将被利用，以证明最高的lyapunov指数在重新规范化后大或等于次移拓扑因子的顶部指数。为了获得替代子缩合因子的结果，我们定义了一种特殊的总和，这是扭曲的Birkhoff总和的多版本。对于thue-morse替代的特定情况，我们得出指数为零，我们给出了扭曲的Birkhoff总和的显式下指数绑定，并且我们对亚转移拓扑因子也这样做。
The present paper explores the spectral cocycle, defined by A. Bufetov and B. Solomyak, in the special case of bijective substitutions on two letters, the most prominent example being the Thue-Morse substitution. We derive an explicit subexponential behaviour of the deviations from the expected exponential behavior. Moreover, these sharp bounds will be exploited to prove that the top Lyapunov exponent is greater or equal to the top exponent of the subshift topological factors after a renormalization. In order to obtain such results for the substitutive subshift factors, we define a special kind of sum, which is a multiple version of the twisted Birkhoff sum. For the particular case of the Thue-Morse substitution, we derive that the exponent is zero, we give an explicit subexponential bound for the twisted Birkhoff sums and we do the same for subshift topological factors.
